sophisticated-dmrg

Source code: https://github.com/simple-dmrg/sophisticated-dmrg/

Documentation: http://sophisticated-dmrg.readthedocs.org/

This code is an expanded density-matrix renormalization group (DMRG) program, based on code written for a tutorial given originally at the 2013 summer school on quantum spin liquids, in Trieste, Italy. It implements DMRG its traditional formulation (i.e. without using matrix product states). DMRG is a numerical method that allows for the efficient simulation of quantum model Hamiltonians. Since it is a low-entanglement approximation, it often works quite well for one-dimensional systems, giving results that are nearly exact.

Typical implementations of DMRG in C++ or Fortran can be tens of thousands of lines long. Here, we have attempted to strike a balance between clear, simple code, and including many features and optimizations that would exist in a production code. One thing that helps with this is the use of Python. We have tried to write the code in a very explicit style, hoping that it will be (mostly) understandable to somebody new to Python.

Features

Beyond the features already existing in simple-dmrg (infinite and finite system algorithms, conserved abelian quantum numbers, and eigenstate prediction), sophisticated-dmrg offers the following improvements:

  • pluggable models
  • choice between open or periodic boundary conditions
  • measurements (assumes operators on different sites commute)
  • site-dependent potential (e.g. to implement disorder)

Future features

Planned and potential features

  • use disk (not RAM) for persistent storage
  • efficient representation of the Hamiltonian (if easily possible in python)
  • time-dependent DMRG
  • custom Lanczos
  • fermions and fermionic Hubbard models
  • models for ladder systems
  • site-dependent hopping terms (e.g. to implement “hopping disorder”)

Highly unlikely future features

  • rewrite in terms of matrix product states
  • non-abelian symmetries (e.g. SU(2))

Authors

  • James R. Garrison (UCSB)
  • Ryan V. Mishmash (UCSB)

Licensed under the MIT license. If you plan to publish work based on this code, please contact us to find out how to cite us.

Contents

Using the code

The requirements are:

Download the code using the Download ZIP button on github, or run the following command from a terminal:

$ wget -O sophisticated-dmrg-master.zip https://github.com/simple-dmrg/sophisticated-dmrg/archive/master.zip

Within a terminal, execute the following to unpack the code:

$ unzip sophisticated-dmrg-master.zip
$ cd sophisticated-dmrg-master/

Once the relevant software is installed, each program is contained entirely in a single file. The first program, for instance, can be run by issuing:

$ python sophisticated_dmrg.py

Note

If you see an error that looks like this:

SyntaxError: future feature print_function is not defined

then you are using a version of Python below 2.6. Although it would be best to upgrade, it may be possible to make the code work on Python versions below 2.6 without much trouble.